my lanlord charges me $5/day EVERYDAY after the 1st .

There is no statutory right to a grace period under a lease agreement.  Instead grace periods are a matter contracted for under the lease.  Where the concept a "5 Day Grace" period originates is the rights under NRS 40.253 et. seq. that a Landlord must serve a Tenant with a "5 Day Pay or Quit" Notice before commencing eviction proceedings. As far a rental increases, as you note, NRS 118A.300 provides  that "[t]he landlord may not increase the rent payable by a tenant unless it serves the tenant with a written notice, 45 days or, in the case of any periodic tenancy of less than 1 month, 15 days in advance of the first rental payment to be increased, advising the tenant of the increase."